A380442 a(n) is the largest Frobenius number of three distinct relatively prime numbers that sum to n.

1, 1, 3, 2, 5, 7, 7, 11, 13, 11, 17, 19, 23, 23, 29, 31, 35, 39, 43, 47, 51, 47, 59, 63, 67, 71, 79, 83, 89, 95, 101, 107, 113, 103, 125, 131, 139, 143, 153, 155, 167, 175, 181, 191, 199, 199, 215, 223, 233, 239, 251, 259, 269, 279, 289, 299, 309, 311, 329, 339

Offset: 9

Author

David A. Corneth, Jul 25 2025

Keywords

• nonn

Comments

6 is the smallest number that can be partitioned into three distinct positive integers excluding n = 1 through 5.

a(6) would be -1 as the only partition of 6 into 3 distinct numbers that are relatively prime are (1, 2, 3) and the largest Frobenius number of that partition is -1.

Similarly a(7) and a(8) would be -1 as all partitions of these numbers into three distinct parts have a 1 in them.

Examples

			a(11) = 3 as the partitions of 11 into 3 distinct numbers that are relatively prime are (2,4,5) and (2,3,6) that have Frobenius number 3 and 1 respectively and their maximum is 3.
		

Links

• Brady Haran and David Eisenbud, The Frobenius Problem (and numerical semigroups) - Numberphile, Numberphile video, 2025

Crossrefs

Cf. A386243.